Download Applications of Random Nonlinear Photonic Crystals Based

Crystals 2012, 2, 1393-1409; doi:10.3390/cryst2041393
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crystals
ISSN 2073-4352
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Review
Applications of Random Nonlinear Photonic Crystals Based on
Strontium Tetraborate
Aleksandr S. Aleksandrovsky 1,2,*, Andey M. Vyunishev 1,2 and Alexandre I. Zaitsev 1,2
1
2
L. V. Kirensky Institute of Physics, Akademgorodok, Krasnoyarsk, Russia;
E-Mails: [email protected] (A.M.V.); [email protected] (A.I.Z.)
Siberian Federal University, Svobodnii 79, Krasnoyarsk, Russia
* Author to whom correspondence should be addressed; E-Mail: [email protected];
Tel.: +7-391-249-4613; Fax: +7-391-243-8923.
Received: 30 July 2012; in revised form: 12 September 2012 / Accepted: 17 September 2012 /
Published: 1 October 2012
Abstract: Properties of strontium tetraborate (SBO) and features of as-grown anti-parallel
domains are summarized. From the point of view of nonlinear optics, these domains form
nonlinear photonic crystals (NPC). Applications of NPC to the deep ultraviolet generation
and fs pulse diagnostics are described. NPC and SBO are prospective media for the
creation of a widely tunable source of fs pulses in the vacuum ultraviolet and for
autocorrelation diagnostics of broadly tunable sources.
Keywords: strontium tetraborate; nonlinear photonic crystals; radiation conversion;
pulse diagnostics
1. Introduction
Spatial modulation of materials’ structure or chemical content on a specific scale is known to be a
method of strong modification of various macroscopic materials’ properties, including mechanical,
electric, magnetic, transport and optical ones. The spatial scale of modulation must be chosen in
consideration of certain physical phenomena influencing corresponding materials’ properties. For
instance, nanoscale spatial modulation in crystals leads to the modification of their electronic band
structure and a number quantum confinement effects arise from this modulation. In optics, this often
leads to the production of material useful for applications, as in case of semiconductor lasers with a
quantum well or quantum dot structure of emitting layer. Another example is the spatial modulation of
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the linear optical properties of a material, the first change being within its refractive index. In this case,
the interference of electromagnetic waves reflected within the material due to steps of refractive index
strongly modifies the spectral dependence of reflection and transmission coefficients. These materials
are commonly called photonic crystals (PC) [1]. They are characterized by the optical band structure
with band gaps and transmission bands where propagation of waves is either forbidden or allowed. The
most common case of these structures is dielectric mirrors and anti-reflection coatings that were
extensively investigated long before the concept of photonic crystals was introduced. When
luminescent centers are introduced to the photonic crystal then the spectrum of their emission becomes
strongly modified, too. The characteristic spatial scale for manifestation of photonic crystal properties
is order of wavelength; however, it also depends on the refractive indexes. The small deviation from
periodicity in modulation strongly influences some properties of a photonic crystal. The most
pronounced case is the photonic crystal with a so-called defect, that is, a single layer with a different
thickness or refractive index. If all the structure is properly matched then additional narrow resonances
will appear within the band gap. These resonances correspond to localized modes of an
electromagnetic field within a PC, the field strength being thousands times higher in the area of defect
than outside the crystal. Minor misfit or randomness of the whole structure leads to radical decrease of
the field strength within defect.
When linear optical properties of the crystal are not modulated but the nonlinear susceptibility
varies alongside the coordinates then this material can be classified as a nonlinear photonic crystal
(NPC) [2]. In this case, the power of a nonlinearly generated field from the NPC undergoes
modification due to the interference of fields generated by different parts of the material. The spatial
scale of nonlinear susceptibility modulation necessary for the manifestation of NPC properties is the
inverse wave mismatch for the specific nonlinear optical conversion process. The spatial modulation
can be fitted in order to enhance certain nonlinear optical conversion process, as described in the very
first paper on nonlinear optics [3]. One can imagine more complex material with simultaneously
modulated linear and nonlinear susceptibilities. These media may be either simple linear PC with the
single defect nonlinear layer or an arbitrary combination of purely linear and nonlinear layers.
Additionally, all these materials are presently classified as NPCs. There are no experimental studies on
these structures to date, so in the following we will use the notation NPC for the materials with
homogeneous linear susceptibility and modulated nonlinear one, unless opposite is specified.
The simplest case of NPC is 1D structures that were widely known as quasi-phase-matching (QPM)
converters long before the emergence of the NPC concept. The main results of studies of QPM
converters can be found in [4]. The direction of those studies was governed by the expected
application, namely, the nonlinear optical conversion of narrowband cw laser radiation in the
crystalline waveguides with periodically inverted domains. The technology of domain inversion is
fairly applicable for ferroelectric crystals, but it is not completely precise and produces domain
structures with regular or random deviations from the exact QPM. Therefore, authors of [4] considered
the influence of these deviations on the spectral dependence of generated power. This dependence for
exact QPM structure with thickness of domains d0 = π/Δk(λ0) is approximately described by (sin(x)/x)2
function, where x = [Δk(λ) − Δk(λ0)]d0N/3.5, N being the number of domains. It was shown [4] that in
case of special kind of deviations this spectral dependence becomes modified and can be, for instance,
a triangular or quasi-rectangular shape.
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During the last decade a new trend in the NPC studies emerged that was connected with the interest
to new materials with high degree of randomness in the spatial modulation of nonlinear susceptibility.
These materials are mainly ferroelectrics with natural structure of anti-parallel and arbitrary sized
domains, or polycrystalline materials. Comprehensive analysis of the most of these studies can be
found in several reviews (see, e.g., [5]), so we will mention only main features of random nonlinear
media. For such media, a new type of phase matching—random quasi-phase-matching (RQPM) [6], or
stochastic QPM [7]—was discovered. It was experimentally demonstrated that in the polycrystalline
nonlinear medium consisting of randomly sized and oriented small single crystals, the maximum
frequency conversion is attained in the case when the average size of a crystal coincides with the
coherence length for the nonlinear conversion process [6]. It was found that while in perfect QPM the
power generated in a nonlinear conversion process grows quadratically with the length of the NPC,
random nonlinear media demonstrate linear power growth with the length at the scale when medium
length exceeds the characteristic randomization length. Random nonlinear crystals were found to be
excellent materials for implementation of so-called nonlinear diffraction (NLD), a kind of
non-collinear phase matching when wave mismatch is compensated by the reciprocal superlattice
vector (RSV) arising from Fourier transform of the nonlinear susceptibility function on the coordinate.
Attractiveness of random nonlinear media for nonlinear diffraction is due to the fact that the angle of
nonlinear diffraction is determined by refractive indices, while the power of nonlinearly diffracted
radiation is determined by Fourier amplitudes corresponding to the RSV required to enable
non-collinear phase matching. So, in random media one can find a necessary RSV for a broad range of
wavelengths [8] or for arbitrary direction of propagation [9]. As a result, complete conversion of the
spectrum of broadband femtosecond pulses in 2D NPC of strontium barium niobate (SBN) crystal was
obtained [8]. The spectral dependence of RQPM in the case of strongly randomized crystal was found
to be consisting of large number of superimposing peaks [10] that cover the range from near infrared
into near UV (on the scale of fundamental wavelengths). Spectral features of both RQPM and random
NLD can be briefly described by the statement: “Random media gains tunability for the price of
efficiency” [8], that is, efficiency obtainable in a regular structure for narrow bandwidth is distributed
over wider spectrum when we have random nonlinear medium.
In recent years, researchers were interested not only in natural random media but also in artificial
random media; that is, in the domain structures that contain several superimposed spatial modulation
frequencies [11,12]. Nonlinear optical properties of such structures must be similar to those of random
structures. Most promising material for the formation of artificial random structures is lithium niobate,
since artificially formed domains in SBN are shown to be unstable [13].
2. Orthorhombic Strontium Tetraborate (α-SBO)
Most of random nonlinear materials investigated up to date are ferroelectrics and formation of
random NPC structure in them occurs during the phase transition from paraelectric higher-symmetry
phase. The loss of some elements of symmetry group of the unit cell of paraelectric phase is
accompanied by formation of anti-parallel domains as if the whole crystal would preserve the
symmetry of the paraelectric phase. On the microscopic scale, the process of domain formation at the
temperature of phase transition is governed by such factors like defects, impurities etc. As a result,
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domains formed in the ferroelectric phase can be either randomized or highly ordered, depending on
degree of microscopic defect randomness.
On the other hand, most ferroelectric materials are not transparent in the ultraviolet, and the results
obtained with random media based on them are inapplicable for this spectral range. For instance, most
widely studied SBN is transparent down to 400 nm, and the shortest wavelength for lithium tantalate is
270 nm. Nonlinear optical generation in the deep ultraviolet (DUV) and vacuum ultraviolet (VUV) is
possible with the help of various borate crystals in the angular phase matching [14], but continuously
tunable nonlinear optical conversion to these spectral ranges meets difficulties and limitations. At the
same time, some possible applications in industry and science still require new laser sources in
DUV/VUV. An attractive possibility is to create powerful femtosecond sources at 193 and 157 nm;
this could be implemented using a combination of femtosecond seed pulses at the wavelengths falling
into the bandwidths of corresponding excimer molecules and excimer amplification modules.
Alternatively, an all-solid-state source at 193 nm in competition with excimer laser is desirable, and
the latter problem was addressed in [15]. The authors of this study managed to create artificial NPC
structure in crystalline quartz that is not a ferroelectric but can be mechanically twinned due to
favorable symmetry properties of its elastic compliance tensor. Another possible medium for DUV and
VUV is orthorhombic strontium tetraborate (α-SBO or simply SBO), which is transparent down to
125 nm [16]. This crystal belongs to mm2 point symmetry class, and the crystallographic axes notation
used below corresponds to the unit cell parameters а = 4.4145(4) Å, b = 10.6827(10) Å, c = 4.2234(4) Å.
Nonlinear susceptibility of SBO is the highest among all nonlinear crystals transparent below 270 nm,
but birefringence is too small to ensure angular phase matching. Nevertheless, coherent radiation at
125 nm was generated in this crystal via a non-phase-matched nonlinear frequency doubling, and the
possibility for autocorrelation of measurements was demonstrated [16]. SBO is not a ferroelectric, as
all other borates. The crystal structure of SBO contains only tetrahedrally coordinated boron ions that
form continuous boron-oxygen network. This network seems to be extremely stable against switching
of the static polarization direction. The properties of SBO crystal structure and the possibility for
inverted domain formation were theoretically investigated in [17]. The crystal structure of SBO was
found to be close to certain higher-symmetry structure with two minima for boron atoms. Possible
domain inversion would take place in case of displacement of boron atoms from one of these minima
to another; however, the energy corresponding to this displacement is in the order of 5000 K.
However, it was found experimentally [9,18] that as-grown boules of SBO obtained via the
Czochralski method contain domain structures comprised of anti-parallel domains. An example of such
a structure is presented in Figure 1. Compared with known ferroelectric crystals, these domain
structures occupy only part of grown crystal. At the same time, the shape and orientation of domains is
identical to that of well-known ferroelectric crystal potassium titanyl phosphate (KTP), namely,
domains have the form of sheets perpendicular to a crystallographic axis. Static polarization is parallel
to c axis, nonzero nonlinear coefficients of SBO are dcaa, dcbb, dccc, daac, and dbbc, dccc being largest
of them.
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Figure 1. Domain structure in strontium tetraborate visualized by etching. Crystallographic
axes are shown by arrows. Thickness of structure in a direction is 1 mm.
The origin of domains in SBO remains unclear and intriguing from a theoretical point of view.
However, starting with experimental facts, we can state that it is connected with an instability of the
position of one of ions, most likely strontium, on the interface between growing crystal and the melt.
Two possible minima of potential energy probably exist for this ion, depending on the process of
boron-oxygen network formation. In completely formed network the position of strontium is strictly
determined and if all boron ions occupy proper minima in the process of network formation, then
strontium ions are likely to occupy main potential minimum position, and domain-free crystal structure
keeps forming. If some boron ions inside incompletely formed network are in the position of
secondary minimum, then adjoining strontium ion can occupy its secondary minimum displaced from
the main minimum in the direction of c axis. In this case, the seed of an inverted domain forms, and
subsequent atomic layers can follow the crystal structure corresponding to inverted orientation of
atoms in the unit cell. Such kind of instability is rather common for the formation of defects in the
process of growth of various crystals, so we must deduce that in case of SBO this instability leads to
rather rare consequence like formation of domain structures. To our knowledge, SBO is the only
non-ferroelectric crystal where such domain structures are formed during controlled single
crystal growth.
All the samples studied in this paper are obtained via common Czochralski technique. The seed
crystal was a domain-free one and was oriented along b axis in the direction of pulling. The starting
temperature on the melt surface for all growth experiments was 1000 °C, the seed rotation rate was
10 rpm, the pulling rate was 2.4 mm/day, and the cooling rate was 1 °C/day. However, since
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microscopic growth instability plays its role in domain formation, minor uncontrollable deviations of
local parameters on the surface between the crystal and the melt have led to variation of domain
structure and nonlinear optical behavior of the samples obtained in separate growth experiments, as
described below.
The dimensions of domain structures obtainable in SBO can be as large as 1 × 1 cm in the
directions of b and c axes. The thickness of the region containing domains in the direction of a axis can
be several millimeters; however, the thickness of individual domains in this direction is highly
randomized. The largest domains within the structure can be more than one hundred microns, while
smallest detected domains are less than hundred nanometers thick. This explains why RSV spectrum of
NPC SBO is smeared over extremely large spectral range with corresponding overall decrease of RSV
amplitudes. Hence, possible applications of NPC SBO are different the conversion processes of
broadband widely tunable laser sources, preferentially femtosecond ones. For fs pulses, radiation
damage threshold becomes higher than in nanosecond pulsewidth scale, and the RSV spectrum
smearing can be compensated by fundamental wave intensity. Special interest can be in the creation of
widely tunable source over the vacuum ultraviolet.
3. Applications of NPC SBO
3.1. Generation of Deep UV Radiation in NPC SBO
Existing crystal-based nonlinear frequency converters of laser radiation to the deep and vacuum
ultraviolet employ angular phase matching [14]. This kind of phase matching commonly provides the
highest efficiency; however, typically it requires a sum frequency conversion scheme with additional
tunable parametric oscillator. Generated power strongly depends on the propagation angle, which must
be accurately tuned in accordance with the tuning of input laser frequencies. The effective nonlinear
coefficient typically decreases with the tuning, as well. All these restrictions limit the spectral region of
tuning obtainable in a single nonlinear crystal converter. The features of random NPC converters are
quite different, as was established in [10] as regards frequency doubling of narrowband nanosecond
pulses. Radiation from a Nd:YAG laser (Lagraph LTI-245, pulse duration 15 ns) was initially
frequency doubled, and unfocused radiation at 532 nm with divergence 3 mrad was used as
fundamental radiation for the next frequency doubling process in NPC SBO. The angular dependence
of the second harmonic at 266 nm for a highly randomized NPC sample consisting of 3 mm thick
domain-free crystal and 2 mm thick NPC (Figure 2) radically differs from that of a 0.431 mm thick
single domain sample shown in the inset in the identical power scale, both in the amplitude and in the
characteristic angular variation scale. One common feature can be found; namely, decreasing of
angular width of oscillation on the growth of rotation angle. In both cases the reason for this behavior
is the interference of the contributions from different layers (coherent-length-thick ones in case of
single domain sample). For a single domain sample, observed angular oscillations are known as Maker
fringes. In analogue, angular behavior of second harmonic in NPC can be considered as
“Random Maker fringes” (RMF). They are strongly distorted in amplitude and angular shape reflecting
RSV spectrum in NPC. Upon tuning the wavelength of fundamental, RMF will behave similar to
common Maker fringes, i.e., minimum at zero angle will turn to maximum and so on (Figure 3).
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Figuree 2. (a) Angular depenndence of thhe second harmonic
h
foor nonlinearr photonic crystals
c
(NPC)) and stronttium tetraboorate (SBO
O); (b) Mak
ker fringes for single ddomain sam
mple of
SBO. Input radiaation (532 nm) directtion k, polaarization off input radiiation and second
harmoonic (266 nm
m) E.
Figure 3. Randdom Maker fringes for NPC SBO calculated by
b varying tthe wavelen
ngth.
Direct prresentation of the RS
SV spectrum
m is the dependence
d
of the seecond harm
monic on thhe
fu
fundamental
l wavelenggth (Figuree 4). This graph cleearly demoonstrates thhe result of
o excessivve
r
randomizatio
on that leadds to a num
mber of relatively narrrow peaks covering laarge spectraal area. Succh
p
properties
arre hardly thhe best fit for
fo any definnite applicaation. Howeever, a num
mber of nonllinear optical
p
processes
caan be enhannced in thee same NPC
C sample. All
A our sam
mples show experimenttally verifieed
e
enhancemen
nt of very different nonlinear
n
o
optical
proccesses, botth for wideely tuned infrared annd
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ultraviolet fundamental wavelengths. For case of infrared fundamental wavelengths enhancement of
efficiency is observed in the same sample for both RQPM and NLD geometries. Enhancement of NLD
requires thinner domains in NPC than RQPM at the same fundamental wavelength. As a result, smaller
enhancement is expected for ultraviolet fundamental wave in NLD than in RQPM.
Figure 4. Spectral dependence of the second harmonic for a sample of NPC SBO (blue)
and single domain sample (black) calculated by varying the fundamental wavelength. Real
domain structure of NPC SBO mapped via optical microscopy was used in the calculation.
Tunable generation of DUV in NPC SBO was investigated [19] using a femtosecond oscillator
(Spectra Physics Tsunami, pulse duration 40–90 fs) of the lowest power class as the starting source of
radiation. At the first stage, radiation was converted into the second harmonic using a traditional
angularly phase matched BBO converter. The spectrum of the second harmonic pulses was smooth
with a width of 2 nm. This radiation with an average power up to 135 mW was focused into the NPC
SBO with the intensity up to 300 MW/cm2 in the direction of RQPM. The doubling of the frequency of
input radiation in NPC SBO resulted in generation of DUV in the region of 200 nm. The spectra of
DUV were not smooth but contained multiple peak structures with the characteristic width of
individual peak in the order of several tenths of a nanometer (Figure 5). These structures are found to
be independent of the power of input radiation and therefore they cannot be due to any process of the
nonlinearity higher than the second one. Obviously, they are the manifestation of the multiple peak
structure seen in the spectrum in Figure 4. Different panels in Figure 4 show spectra obtained in the
NPC samples from different growth experiments. These samples had different domain structures but
the control of this structure by the growth conditions is presently above our experimental abilities. The
quality of spectra is not perfect, but comparison of spectra from samples S2 and S4, from one side, and
those from samples S7 and S8, from the other side, show that the degree of spectra deterioration can be
in principle controlled by the growth process of SBO crystals using more advanced growth
installations. From Figures 4 and 5, one can expect that DUV tuning curve might exhibit strong
influence of the same multipeak structure. However, for typical bandwidth of input femtosecond pulse
and NPC structure typical for SBO it was found that it is not so.
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Figure 5. The spectra of deep ultraviolet (DUV) generated in several samples (S2, S4, S7,
S8) obtained in separate growth experiments.
DUV tuning curves (Figure 6) were obtained for several samples at the fixed position of the NPC
by a tuning oscillator and BBO doubler. Continuous tuning can typically be obtained in the range from
232.5 to 187.5 nm. The upper limit of this range could be easily shifted approximately to 250 nm, in
view of the Tsunami tuning range. The lower limit was determined by the absorption in the air and
surely can be extended to shorter wavelengths, probably below 180 nm, since no signs of absorption in
NPC material were found. Among investigated samples, there is considerable difference in the
efficiency in the order of ten that must be connected with the variativity of as-grown NPCs. Maximum
generated power at 200 nm in the order of 1 μW. The dependence of generated power on the input
power was experimentally found to be quadratic up to an input intensity of 300 MW/cm2 [20], so to
increase generated power by 10–100 is expected in view of the high radiation breakdown threshold of
SBO. The decrease of generated power at shorter wavelength is mainly due to air absorption. The
decrease of RSV amplitudes is present in this spectral region too, but it plays a secondary role. The
tuning curve bears no signs of narrow multiple peak structure in Figure 5, but variations in RSV
amplitudes at the scale of several nanometers are well observable.
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Figuree 6. DUV tuning
t
curvves for seveeral samples (S2, S4, S7, S8) obtained in seeparate
growthh experimeents. DUV power is normalized
d to the square of tthe power of the
fundam
mental beam
m.
Spectral and angularr dependencces of geneerated poweer in NPCs are connected through
h the conceppt
o the NPC band struccture [10,211]. Peaks obbserved in both depenndences cann be associaated with thhe
of
s
same
set off RSV. An example
e
off angular deependence of
o DUV poower is pressented in Fiigure 7. Thhis
c
curve
is in general
g
term
ms symmetriical with resspect to the case of norrmal incidennce, deviatio
ons from thhis
s
symmetry
b
being
due to the insstability off some exp
perimental parameterss, i.e., the temperaturre
f
fluctuations.
. The range of power variation
v
in the order of three withhin 30 degreees can be considered
c
a
as
s
super-critica
al angular sensitivity
s
o RQPM. Similarly, slow quasii-monotonicc decrease of generateed
of
p
power
with its
i central wavelength
w
QPM.
can be treatted as superr-critical speectral sensittivity of RQ
Figure 7. An
A examplee of angular dependencee of DUV generated
g
inn NPC SBO.
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3.2. Fs Pulses Diagnostics Using NPC SBO
Pulse diagnostic experiments were conducted for fundamental radiation of the Ti:sapphire laser, in
order to investigate all the details of NPC SBO operation as the nonlinear material for these
purposes [22,23]. A common autocorrelation optical scheme was used to form two intersecting beams
of the diagnosed radiation with controllable delay between pulses. In this geometry, both collinear and
non-collinear second harmonic generation takes place, but only non-collinear interactions are useful
for pulse diagnostics. For non-collinear interactions, both RQPM and NLD geometries are usable for
diagnostics. In the former case, to ensure a noticeable RQPM effect for NPC SBO samples in our
disposal, the bisector of fundamental beams must coincide or be in the vicinity of the perpendicular to
the domain walls. For NLD geometry, the bisector of fundamental beams must lie in the plane of
domain walls or be in the vicinity of this plane. In these two cases, nonlinear interaction of intersecting
beams employs different parts of RSV spectrum, and it is interesting to compare accuracy and
signal-to noise ratio for these two possible schemes. A comparison with angular phase matching was
done using properly cut BBO reference crystal.
3.2.1. RQPM Scheme
The idea to use RQPM in strongly randomized structures may lead to doubts, due to multiple peak
structures expected in autocorrelation signal, since it is typically recognized that for accurate
measurement all the spectral components must fall into the phase matching width. Typical
autocorrelation curves obtained with RQPM scheme and with reference crystal are presented in
Figure 8. It demonstrates excellent agreement between the reference crystal and NPC, despite the
doubts mentioned above. Measurement of the second harmonic spectra of autocorrelation signal and
single beam signal (Figure 9) reveals that the autocorrelation signal has a much wider spectrum than
the single beam signal, which favors the accurate determination of the pulse duration. The
modification of the spectrum in autocorrelation beam can be explained by the geometry of interaction
of two focused intersecting fundamental beams. The signal-to-background ratio in the case of RQPM
is found to be in the order of 3000, while for angular phase matching in BBO reference crystal it is
close to 20000. At the same time, the background level in the experiment with reference crystal was
much higher than in that with NPC SBO, while in the case of NPC SBO the background noise was
determined by the intrinsic noise of detector. Therefore, using the detector with lower intrinsic noise will
increase the signal-to-background ratio in the case of NPC SBO.
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Figure 8. RQPM autocorrelation trace of Tsunami oscillator measured with NPC SBO
(blue) and BBO (black). Central wavelength 780 nm. SBO: pulse duration 83.3 fs; power
3.49 microwatts; SNR-2992; BBO: pulse duration 83.7 fs; power 929.9 microwatts;
SNR-15079.
Figure 9. Spectra of autocorrelation signal (a) and single-beam second harmonic (b).
The dependence of pulse duration on the oscillator central wavelength (Figure 10) was obtained
throughout all available tuning range of Ti:sapphire oscillator 710–930 nm at fixed position of NPC.
Signal-To-Background ratio was in the order of several thousand for all measured points. This admits
unique spectral insensitivity of random NPC already pointed out in the case of DUV generation
experiments. NPC structures in SBO are known to be highly randomized in a axis direction. Due to
this fact, one may expect that the displacing the NPC along this axis may influence accuracy of
measurements. Figure 11 presents the results of the spectral measurement of autocorrelation beam
obtained in the course of scanning the NPC along the a axis, while all the rest parameters of the optical
scheme remained unchanged. Really, the variation in the spectra is rather noticeable. However,
autocorrelation traces taken in three positions of NPC indicated by vertical dashes show the same
results for the pulse duration. Additionally, this measurement reveals evident “wavy” spatial variation
of the NPC structure that arises from some morphological inhomogeneity associated with the growth
process of strontium tetraborate crystal sample under study.
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Figure 10. Pulse duration of Tsunami oscillator measured with NPC SBO throughout the
tuning range at fixed angular position of the crystal.
Figure 11. Variation of autocorrelation beam spectra on the NPC position. (a) Net data;
(b) Data normalized to the maximal value in every section of constant coordinate.
3.2.2. Autocorrelation Measurements Using Nonlinear Diffraction from Virtual Beam
Nonlinear diffraction from virtual beam (NLDVB) was recently demonstrated [24]. Nonlinear
diffraction from virtual beam is attractive for autocorrelation measurements since the spectral scale of
signal variation in the NLD second harmonic generation is larger than within RQPM for typical NPC
SBO structures. Depending on the mutual orientation of domain walls plane and beams intersection
plane, two different patterns can be obtained in 1D NPC. When these planes are parallel, then the
autocorrelation beam does not coincide with any other beams and is always observed separately. When
aforementioned planes are perpendicular as in case of normal incidence, there is an overlap of the
autocorrelation beam and one of the beams diffracted from a single fundamental beam. In SBO these
schemes employ nonlinear coefficients dcaa and dccc, respectively. In view of larger value of dccc, the
latter scheme must be more efficient and enable larger dynamic range of measurements. To avoid
beam overlapping, NPC must be rotated off the normal incidence position around the axis
perpendicular to the intersection plane. This rotation does not affect the effective nonlinear coefficient
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thhat remainns to be eqqual to dcccc. The anggle of rotattion can be found exxperimentallly from thhe
c
consideratio
ons of minim
mizing the overlap
o
conttribution to the backgroound and m
maximum co
ontribution of
o
R
RSV
spectruum. Sufficieent rotationn angle valuue for our saamples wass found to bbe of below
w ten degreees.
T schemee of experiimental sett-up is preesented in Figure 12. Typical aautocorrelatiion curve is
The
p
presented
inn Figure 13 in compariison with reeference cry
ystal. The agreement
a
iss as good as
a in the casse
R
RQPM
scheeme. The baackground-tto noise ratiio was 1600
0, that is appproximatelyy two times smaller thaan
inn RQPM geometry.
g
T
This
differeence, in ourr opinion, is
i not funddamental annd can be decreased
d
b
by
c
careful
adjuustment off the experrimental seetup. In caase of NL
LDVB, the propagatio
on angle of
o
a
autocorrelati
ion beam changes when
w
tuninng the ceentral frequuency of the fundam
mental. Thhe
a
autocorrelati
ion measurrements in the coursee of tuning
g the centrral frequenncy of the fundamental
r
radiation
aree, therefore,, slightly more
m
compliccated since it is necesssary to monnitor this change, but foor
laarge aperturre detector this
t difficullty is not sevvere.
Figuree 12. Optical scheme of autocorrrelation meaasurement inn nonlinearr diffraction
n from
virtuall beam (NL
LDVB) geom
metry. 1-Tssunami osciillator; 2-beeamsplitter; 3-mirror; 4-delay
4
line; 5-focusing leens; 6-NPC SBO; 7-BG
G39 filter; 8-918D-UV
8
V-OD3 sensoor.
VB autocorrrelation trace of Tsunaami oscillattor measureed with NPC
C SBO
Figuree 13. NLDV
(blue) and BBO (black).
(
Cenntral wavelength 840 nm.
n SBO: pulse
p
duratiion 75.7 fs; power
5.99 microwatts;
m
; SNR-18777; BBO: pulse duraation 77.0 fs; power 770 micro
owatts;
SNR-117510.
Crystals 2012, 2
1407
4. Conclusions
An overview of recent results on properties and nonlinear frequency conversion processes in NPC
SBO is presented. Angular dependence of nonlinear optical conversion efficiency is treated like
“random Maker fringes”. The variativity of NPC structures obtainable in SBO indicates that spectra of
generated radiation can be controlled in the process of NPC growth. Both RQPM and NLDVB
schemes are shown to be equally useful for fs pulse diagnostics. Spatial distribution of RSV in NPC is
revealed by investigations of generated spectra. Random nonlinear photonic crystals of strontium
tetraborate are found to be useful for two applications, namely, generation of DUV radiation and
autocorrelation measurements. Nonlinear optical converters based on NPC SBO are featured by unique
tolerance to spectral and angular detuning. Due to transparency in the VUV, NPC and SBO are
prospective for creation of widely tunable femtosecond source in this spectral region.
Acknowledgments
The work was supported by the Ministry of Education and Science of Russian Federation
(Contracts 16.740.11.0150 and 14.B37.21.0730, and Grant 2.1.1/3455), by RFBR Grant 12-02-31167,
by the Russian President Grant SS-1044.2012.2, by RAS Projects 29 and 31, by PSB RAS Projects
2.5.2 and 3.9.5, by SB RAS Projects 43 and 101, and by SFU Grant F12.
Conflict of Interest
The authors declare no conflict of interest.
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